Q1. Given n+1 data pairs, a
unique polynomial of degree ____ passes through the n+1 data
points.n+1nn or less
greater than n

Q2. Given
the two points
, the linear Lagrange polynomial
that passes through these two points is given by

Q3. The
Lagrange polynomial that passes through three data points is given by

x

15

18

22

y

24

37

25

The
value of
at
x = 16 is

–0.071430
0.50000
0.57143
4.3333

Q4. The
following data of the velocity of a body is given as a function of time.

Time
(s)

10

15

18

22

24

Velocity
(m/s)

22

24

37

25

123

A
quadratic Lagrange interpolant is found using three data points, t=15, 18 and
22.From this information, at what of the times given in seconds is the velocity of the
body 26 m/s during the time interval of t=15 to 22 seconds.

20.173
21.858
21.667
22.020

Q5. The path that a
robot is following on a x-y plane is found by interpolating four data
points as

x

2

45

5.5

7

y

7.5

7.5

6

5

The
length of the path from x = 2 to x = 7 is

Q6. The
following data of the velocity of a body is given as a function of time.

Time
(s)

0

15

18

22

24

Velocity
(m/s)

22

24

37

25

123

If
you were going to use quadratic interpolation to find the value of the velocity
at t=14.9 seconds, what three data points of time would you choose for
interpolation? Justify your answer.